Predator prey modeling at the molecular level: Analytical considerations about the coupling of biochemical events during photo-chemo therapy and cell survival probability

Photodynamic therapy (PDT) is a promising modality in cancer treatment that involves localized photo-irradiation of dye sensitized tissue to kill cancer cells. A photosensitizer is administered to the patient either locally or systematically by one of several routes (e.g., topical, oral, intravenous) and after a predetermined (appropriate for optimal bio-distribution) time interval, the treatment site is irradiated with visible or near-infrared light. The light is absorbed by this photosensitizer which initiates photochemical reactions leading to the eradication of the tumor cells. Based on previous models of detailed molecular pathways and biochemical events induced by PDT treatment leading to cell death that can occur through a multiplicity of different mechanisms such as apoptosis, necrosis and autophagy, a cell survival probability equation is introduced as a measure of the PDT tumor cell killing, which can be difficult to quantify through experimental verification of the molecular concentrations of the cytotoxic agents. This report is an attempt towards coupling the single cell survival probability to the molecular concentrations, which can be useful in the design of predictive treatment, with models such as cellular automata.